Difference between revisions of "Subgroup"
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| − | A [[subset]] ''H'' of a [[group]] (''G'',<math>\cdot</math>) is called a '''subgroup''', if (''H'',<math>\cdot</math>) is itself a group. | + | A [[subset]] ''H'' of a [[Group (mathematics)|group]] (''G'',<math>\cdot</math>) is called a '''subgroup''', if (''H'',<math>\cdot</math>) is itself a group. |
| + | ==Simple Examples== | ||
| + | # <math>(2\mathbb{Z},+)</math> is a subgroup of <math>(\mathbb{Z},+) </math> | ||
| + | # <math>(\mathbb{Z},+) </math> is a subgroup of <math>(\mathbb{Q},+) </math> | ||
| + | # <math>(\mathbb{Q}^+,\cdot) </math> is a subgroup of <math>(\mathbb{R}^+,\cdot) </math> | ||
[[Category:Algebra]] | [[Category:Algebra]] | ||
